Partially ordered structures are ubiquitous in theoretical computer science. From knowledge representation to abstract interpretation in static analysis, from resource modelling to protocol or access rights formalization in formal security, the list of applications is enormous. Being able to formally reason about transition systems over posets therefore seems important, but has not been systematically developed. The natural formalism to reason about transition systems is undoubtedly the class of modal logics. However, most are tailored to transition structures over sets. This is a direct consequence of the fact that most modal logics are boolean. Positive modal logic is the exception, and is most naturally interpreted in partially ordered Kripke structures (see for example [1]}, [2]}).
